3L 10s

"3L 10s" is a MOS scale pattern with 3 large steps and 10 small steps. Some notable temperaments that form a MOS with this pattern are magic and würschmidt.

Of course, magic[13] is still slightly improper and würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13 tone per octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13 tone circles favor multiple times over.

1\3										400
									13\40	390
								12\37		389.189
							11\34			388.235
									32\99	387.879	Whirrschmidt
								21\65		387.692	Worschmidt
									31\96	387.5	Würschimdt
						10\31				387.097	Würschimdt
							19\59			386.441	Sulis
					9\28					385.714
				8\25						384	Marveltri
			7\22							381.818	Sorcery
					20\63					380.952
						33\104				380.769	Optimal patent val for 11-limit magic
				13\41						380.488	Optimal patent val for 13-limit magic
					19\60					380	Optimal patent val for 5-limit magic
										379.408
		6\19								378.947
										377.967
				17\54						377.778
						45\143				377.622
								118\375		377.6
									191\607	377.595
							73\232			377.586
					28\89					377.528
			11\35							377.143
	5\16									375	Boundary of propriety (Smaller generators are proper)
										373.6775
			14\45							373.333
					37\119					373.109
							97\312			373.077
									254\817	373.072
								157\505		373.069
						60/193				373.057
				23\74						372.973
										372.812
		9\29								372.414
			13\42							371.429
				17\55						370.909
					21\68					370.588
						25\81				370.37
							29\94			370.213
								33\107		370.0935
									37\120	370
4\13										369.231